Applications in Multivariate Time Series Analysis and Forecasting: SSA

Singular Spectrum Analysis (SSA) is a powerful method of time series analysis and forecasting. It combines advantages of many other methods, such as Fourier and regression analyses, with simplicity of visual control aids. The basic SSA algorithm for analyzing time series consists of:

• Transformation of the time series into a matrix using the moving window;
• Singular Value Decomposition (SVD) of this matrix;
• Reconstruction of the original time series based on selected eigentriples.

The two techniques used in SSA (SVD and the reconstruction procedure) are optimal in a natural class of techniques of multivariate analysis. The result of the SSA processing is a decomposition of the time series into several components, which can often be identified as trends, seasonalities and other oscillatory series, or noise components. This decomposition initializes forecasting procedures for both the original time series and its components. The method can be naturally extended to multidimensional time series and to image processing.

The method is a powerful and useful tool of time series analysis in meteorology, hydrology, geophysics, climatology, economics, biology, physics, medicine and other sciences. It can be used for the series that are short and long, one-dimensional and multidimensional, stationary and nonstationary, almost deterministic and noisy.

Current interests in the cluster concentrate around the following topics:

• Perturbation analysis in SSA and related techniques
• Multivariate SSA and its applications to econometrics
• Application of SSA to the analysis of images
• SSA as a change-point detection technique
• Sensitivity of SSA forecasting formulas to the noise level
• Application of SSA for finding structure in human genome studies
• Comparison of SSA with ARIMA and other standard techniques of time series analysis and forecasting

Cardiff investigators

• Prof Anatoly Zhigljavsky
• Dr Valentina Moskvina
• Dr Andrey Pepelyshev
• Dr Karl Michael Schmidt
• Mr Hossein Hassani
• Dr Jonatan Gillard
• Dr Saeed Heravi

Collaborators

• Prof Kerry Patterson
• Dr Nina Golyandina
• Dr Vladimir Nekrutkin
• Dr Licesio Rodríguez Aragón
• Dr Theodor Alexandrov
• Mr Konstantin Usevich

Selected publications

Goljandina N.E., Nekrutkin V.V., Zhigljavsky A.A. (2001) Analysis of Time Series Structure: SSA and related technique, Chapman & Hall / CRS, Boca Raton, xii+306pp / read at google, buy at amazon

Danilov D., Zhigljavsky A.A., ed. (1997) Principal Components of Time Series: The Caterpillar Method. University of St.Petersburg, 308 pp.

Hassani H., Zhigljavsky A.A. Forecasting European Industrial Production with Singular Spectrum Analysis. Int. Journ of Forecast. 2008, In press

Moskvina V.G. and Zhigljavsky A.A. (2003) An algorithm based on singular spectrum analysis for change-point detection, Communication in Statistics - Simulation and Computation, v. 32, No. 2, 319-352.

Moskvina V.G. and Zhigljavsky A.A. (2003) An algorithm based on singular spectrum analysis for change-point detection, Communication in Statistics - Simulation and Computation, v. 32, No. 2, 319-352.